Generalized Chern–Pontryagin models

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2024-11, Vol.84 (11), p.1199-11, Article 1199
• Main Authors: Nascimento, J. R., Petrov, A. Yu, Porfírio, P. J., da Silva, Ramires N.
• Format: Article
• Language: English
• Subjects: Astronomy; Astrophysics and Cosmology; Black holes; Degrees of freedom; Elementary Particles; Gravitational fields; Gravitational waves; Gravity; Hadrons; Heavy Ions; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Parity; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article; Relativity; Scalars; Schwarzschild metric; String Theory; Symmetry; Tensors; Theory of relativity; Topology
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-024-13607-7

We formulate a new class of modified gravity models, that is, generalized four-dimensional Chern–Pontryagin models, whose action is characterized by an arbitrary function of the Ricci scalar R and the Chern–Pontryagin topological term ∗ R R , i.e., f ( R , ∗ R R ) . Within this framework, we derive the gravitational field equations and solve them for the particular models, f ( R , ∗ R R ) = R + β ( ∗ R R ) 2 and f ( R , ∗ R R ) = R + α R 2 + β ( ∗ R R ) 2 , considering two ansatzes: the slowly rotating Schwarzschild metric and first-order perturbations of Gödel-type metrics. For the former, we find a first-order correction to the frame-dragging effect boosted by the parameter L , which characterizes the departures from general relativity results. For the latter, Gödel-type metrics hold unperturbed, for specific sort of perturbed metric functions. We conclude this paper by displaying that generalized four-dimensional Chern–Pontryagin models admit a scalar-tensor representation, whose explicit form presents two scalar fields: Φ , a dynamical degree of freedom, while the second, ϑ , a non-dynamical degree of freedom. In particular, the scalar field ϑ emerges coupled with the Chern–Pontryagin topological term ∗ R R , i.e., ϑ ∗ R R , which is nothing more than Chern–Simons term.